The side length of an equilateral triangle is 20cm. How do you find the length of the altitude of the triangle?

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Answer 1 · 2018-07-09T12:41:13

I tried this:

Consider the diagram:
enter image source here
we can use Pythgoras theorem applied to the blue triangle giving:

#h^2+10^2=20^2#

rearranging:

#h=sqrt(20^2-10^2)=sqrt(300)=17.3cm#

Answer 2 · 2018-07-09T13:51:51

#17.3cm#

You can use trigonometry to find the altitude (same as height) of the triangle.

In an equilateral triangle, all the sides are equal and all the angles are equal to #60°#

The altitude is the side opposite the #60°# angle

#o/20 = sin 60°#

#o = 20 xx sin60°#

#o = 17.3cm#